Stable flight control method for multi-rotor unmanned aerial vehicle based on finite-time neurodynamics

ABSTRACT

Provided is a stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics, comprising the following implementation process: 1) acquiring real-time flight orientation and attitude data through airborne sensors, and analyzing and processing kinematic problems of the aerial vehicle through an airborne processor to establish a dynamics model of the aerial vehicle; 2) designing a finite-time varying-parameter convergence differential neural network solver according to a finite-time varying-parameter convergence differential neurodynamics design method; 3) solving output control parameters of motors of the aerial vehicle through the finite-time varying-parameter convergence differential neural network solver using the acquired real-time orientation and attitude data; and 4) transmitting results to speed regulators of the motors of the aerial vehicle to control the motion of the unmanned aerial vehicle. Based on the finite-time varying-parameter convergence differential neurodynamics method, the invention can approximate the correct solution of the problem in a quick, accurate and real-time way, and can well solve a variety of time-varying problems such as matrix, vector, algebra and optimization.

TECHNICAL FIELD

The invention relates to the technical field of flight control of unmanned aerial vehicles, in particular to a stable flight control method for orientation and attitude of a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics.

BACKGROUND ART

In recent years, with the increasing development of science and technology, multi-rotor unmanned aerial vehicles have been widely used in many fields, such as military, agriculture, surveillance missions and detection, because of its low cost, flexible flight and simple mechanical structure. In the research field of multi-rotor unmanned aerial vehicles, a key point is the design of its orientation stability and attitude angle stability controller. In practical application, the stability of position and angle is of great significance. Generally, in the case of remote operation, an operator usually manually and remotely controls an unmanned aerial vehicle, and constantly controls and adjusts the position, height, pitch angle, roll angle, yaw angle, etc. to achieve a target position and attitude or complete a target task. Obviously, in this process, it is required that not only the operator should have rich remote operation experience, but also the unmanned aerial vehicle should have good orientation and attitude angle stability and anti jamming capability. This is also the original intention of more and more scholars and researchers who are attracted to further study the design method of unmanned aerial vehicle stability controllers. Although the control of a small multi-rotor unmanned aerial vehicle is relatively simple and convenient, the design method of its orientation and angle stability controller is complex, diverse and fascinating. With the development of research, after realizing simple orientation and attitude control of unmanned aerial vehicles, it is meaningful and practical to provide unmanned aerial vehicles with the ability to follow time-varying target values in order to meet the demand of some complex special tasks. For example, when an unmanned aerial vehicle is used in aerial photography, it is often necessary for the aerial vehicle to photograph in a fixed flight attitude in a predetermined orbit, or to photograph the same object in 360° in a predetermined orbit, etc. Therefore, the controller of the unmanned aerial vehicle must have the ability to follow a time-varying target, that is, the controller must have strong robustness, fast convergence rate and stability, so as to ensure that the unmanned aerial vehicle can effectively follow the time-varying target.

SUMMARY OF THE INVENTION

The objective of the invention is to provide a stable flight control method for a multi-rotor unmanned aerial vehicle in order to solve the above-mentioned defects in the prior art.

The object of the invention can be achieved by taking the following technical solutions:

a stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics, comprising the steps of:

S1, acquiring real-time flight orientation and attitude data of the multi-rotor unmanned aerial vehicle through sensors thereof, and analyzing and processing kinematic problems of the aerial vehicle correspondingly through an airborne processor to establish a dynamics model of the aerial vehicle;

S2, designing a finite-time varying-parameter convergence differential neural network solver for the dynamics model of the multi-rotor aerial vehicle according to a finite-time varying-parameter convergence differential neurodynamics design method;

S3, solving output control parameters of motors of the aerial vehicle through the finite-time varying-parameter convergence differential neural network solver using the acquired real-time orientation and attitude data of the aerial vehicle; and

S4, transmitting the solved output control parameters to speed regulators of the motors of the aerial vehicle to control the motion of the unmanned aerial vehicle.

Further, the analyzing and processing kinematic problems of the aerial vehicle correspondingly through an airborne processor to establish a dynamics model of the aerial vehicle of step S1 specifically comprises: ignoring the effect of air resistance on the aerial vehicle, such that a physical model can be established for the aerial vehicle system:

$\begin{matrix} {{{{\begin{bmatrix} {mI} & 0_{3 \times 3} \\ 0_{3 \times 3} & J \end{bmatrix}\begin{bmatrix} \overset{.}{v} \\ \overset{.}{w} \end{bmatrix}} + \begin{bmatrix} {w \times \left( {mv} \right)} \\ {w \times \left( {Jw} \right)} \end{bmatrix}} = {\begin{bmatrix} F \\ T \end{bmatrix} + \begin{bmatrix} G \\ 0_{3 \times 3} \end{bmatrix}}},} & (1) \end{matrix}$

wherein m is a total mass of the aerial vehicle, I is a 3×3 identity matrix, J is a rotational inertia matrix of the aerial vehicle, v and w are a velocity vector and an angular velocity vector of the aerial vehicle in a ground coordinate system, F and G are an axial component vector of an output resultant force of the motors of the aerial vehicle and an axial component vector of gravity of the aerial vehicle, respectively, and T is a rotational torque vector of the aerial vehicle;

establishing a ground coordinate system X_(G) and an aerial vehicle body coordinate system X_(U), wherein the ground coordinate system and the body coordinate system have the following relationship: X_(U)=KXDG, in which conversion relationship, K is a rotation conversion matrix between the ground coordinate system and the body coordinate system, which can be expressed as

${K = \begin{bmatrix} {C_{\theta}C_{\psi}} & {C_{\theta}S_{\psi}} & {- S_{\theta}} \\ {S_{\phi}S_{\theta}C_{\psi}} & {{S_{\phi}S_{\theta}S_{\psi}} + {C_{\phi}S_{\psi}}} & {S_{\phi}C_{\theta}} \\ {{S_{\phi}S_{\theta}C_{\psi}} - {C_{\phi}S_{\psi}}} & {{C_{\phi}S_{\theta}S_{\psi}} - {S_{\theta}C_{\psi}}} & {C_{\theta}C_{\phi}} \end{bmatrix}},$

wherein C_(θ) represents cos θ(t), S_(θ) represents sin θ(t), θ(t) is the pitch angle, ψ(t) is the yaw angle, and ϕ(t) is the roll angle;

according to the coordinate conversion theory, in a translation direction and a rotation direction of the aerial vehicle, basing on the above physical model, such that the following dynamics equation in the aerial vehicle body coordinate system can be obtained

$\begin{matrix} \left\{ {\begin{matrix} {\overset{¨}{ϰ} = \frac{{u_{1}(t)}\left( {{\cos\;{\phi(t)}\sin\;{\theta(t)}\cos\;{\psi(t)}} + {\sin\;{\theta(t)}\sin\;{\psi(t)}}} \right)}{m}} \\ {\overset{¨}{y} = \frac{{u_{1}(t)}\left( {{\sin\;{\phi(t)}\sin\;{\theta(t)}\cos\;{\psi(t)}} - {\sin\;{\psi(t)}\cos\;{\psi(t)}}} \right)}{m}} \\ {\overset{¨}{z} = {\frac{{u_{1}(t)}\cos\;{\theta(t)}\cos\;{\phi(t)}}{m} - g}} \\ {\overset{¨}{\phi} = \frac{{l \cdot {u_{2}(t)}} + {\left( {J_{y} - J_{z}} \right){\overset{.}{\psi}(t)}{\overset{.}{\theta}(t)}}}{J_{y}}} \\ {\overset{¨}{\theta} = \frac{{l \cdot {u_{3}(t)}} + {\left( {J_{z} - J_{ϰ}} \right){\overset{.}{\psi}(t)}\overset{.}{\phi}(t)}}{J_{y}}} \\ {\overset{¨}{\psi} = \frac{{u_{4}(t)} + {\left( {J_{ϰ} - J_{y}} \right){\overset{.}{\theta}(t)}\overset{.}{\phi}(t)}}{J_{z}}} \end{matrix},} \right. & (2) \end{matrix}$

wherein x, y, z are position coordinates of the aerial vehicle in the world coordinate system, respectively, J_(x), J_(y) and J_(z) are rotational inertia of the aerial vehicle in x-axis, Y-axis and z-axis directions, respectively, l is an arm length, g is gravitational acceleration, synthesized control parameters u₁˜u₄ consist of output thrust of the motors of the aerial vehicle and a synthesized torque, u₁(t) is a resultant force in a vertical ascending direction of the aerial vehicle, u₂(t) is a resultant force in a roll angle direction, u³(t) is a resultant force in a pitch angle direction, and u₄(t) is the synthesized torque in a yaw angle direction.

Further, the designing a finite-time varying-parameter convergence differential neural network solver for the dynamics model of the multi-rotor aerial vehicle according to a finite-time varying-parameter convergence differential neurodynamics design method of step S2 specifically comprises:

by means of the finite-time varying-parameter convergence differential neurodynamics design method, designing a system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄ in respect to the z-axis height z(t), the roll angle ϕ(t), the pitch angle θ(t) and the yaw angle ψ(t), respectively; and

designing the finite-time varying-parameter convergence differential neural network solver according to the obtained system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄, respectively.

Further, the step of by means of the finite-time varying-parameter convergence differential neurodynamics design method, designing a system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄ in respect to the z-axis height z(t), the roll angle ϕ(t), the pitch angle θ(t) and the yaw angle ψ(t), respectively, specifically comprises:

S201, for the z-axis height z(t), according to a set target height value and an actual height value z_(T)(t) in the z-axis direction, defining a deviation function e_(z1) about the actual height value z(t) on a position layer as follows: e_(z1)(t)=z(t)−z_(T) (t) in order to enable the actual value z(t) to converge to the time-varying target value z_(T)(t), designing a neurodynamics equation ė_(z1)(t)=−γ(t)Φ(e_(z1)(t),t) based on a deviation function according to the finite-time varying-parameter convergence differential neurodynamics design method, wherein γ(t)=p+t^(p) is a time-varying parameter representing a regulatory factor for the rate of convergence;

${\Phi\left( {{e_{z1}(t)},t} \right)} = \left. k_{1} \middle| {e_{z1}(t)} \middle| {}_{r}{{{sign}\mspace{11mu}\left( {e_{z1}(t)} \right)} + {k_{2}{e_{z1}(t)}} + k_{3}} \middle| {e_{z1}(t)} \middle| {}_{\frac{1}{r}}{{sign}\;\left( {e_{z1}(t)} \right)} \right.$

according to the deviation function e_(z1)(t)=z(t)−z_(T)(t), ė_(z1)=ż(t)−ż_(T)(t) can be obtained; by substituting e_(z1)(t) and ė_(z1)(t) into ė_(z1)(t)=−γ(t)Φ(e_(z1)(t),t), we can obtain

ż(t)−ż _(T)(t)+(t ^(p) +p)Φ(e _(z1)(t),t)=0;   (3)

the position layer z(t) can converge to the time-varying target value z_(T)(t) in a super-exponential manner within a finite time, however, since equation (3) does not contain relevant information about the control parameters u₁˜u₄, the solution of the control parameters cannot be realized, therefore, it is necessary to further design the deviation function including a velocity layer z(t) and an acceleration layer {umlaut over (z)}(t) thus defining e_(z2)(t)=ż(t)−ż_(T)(t)+(t^(p)+p)Φ(e_(z1)(t),t); according to the finite-time varying-parameter convergence differential neural network design method, the dynamics equation ė_(z2)(t)==γ(t)Φ(e_(z2)(t),t) based on the deviation function can be designed,

${\Phi\left( {{e_{z2}(t)},t} \right)} = {\left. k_{1} \middle| {e_{z2}(t)} \middle| {}_{r}{{{sign}\;\left( {e_{z2}(t)} \right)} + {k_{2}{e_{z2}(t)}} + k_{3}} \middle| {e_{z2}(t)} \right.❘^{\frac{1}{r}}{{sign}\;\left( {e_{z2}(t)} \right)}}$

according to e_(z2)(t)==ż(t)−ż_(T) (t)+(t^(p)+p)Φ(e_(z1)(t),t), the derivative ė_(z2) (t) of the deviation function e_(z2)(t) is known as: ė_(z2)(t)={umlaut over (z)}_(T)(t)±(p+t^(p)){dot over (Φ)}(e_(z1)(t),t)+pt^(p−1)Φ(e_(z1)(t),t) by substituting the above equations about e_(z2)(t) and ė_(z2)(t) into the equation ė_(z2)(t)=γ(t)Φ(e_(z2)(t),t), the following function can be obtained:

{umlaut over (z)}(t)−{umlaut over (z)} _(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(z1)(t),t)+Φ(e _(z2)(t),t)+pt ^(p−1)Φ(e _(z1)(t),t)=0   (4)

when equation (4) is established, the velocity layer ż(t) will converge to ż_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered

E _(z)(t)={umlaut over (z)}(t)−{umlaut over (z)} _(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(z1)(t),t)+Φ(e _(z2)(t),t)+pt ^(p−1)Φ(e _(z1)(t),t)   (5)

in order to obtain an actual model of the neural network, in combination with kinetic equation (2), equation (5) can be rewritten into

E _(z)(t)=a _(z)(t)u ₁(t)+b _(z)(t)   (6)

wherein

${{a_{z}(t)} = \frac{\cos{\theta(t)}\cos\;{\phi(t)}}{m}},$

b_(z)(t)=−g−{umlaut over (z)}_(T)(t) (p+t^(p)){dot over (Φ)}(e_(z1)(t),t)+pt^(p−1)Φ(e_(z1)(t),t)+(p+t^(p))Φ(e_(z2)(t),t) that is, the deviation function about the output control parameter u₁(t) is obtained;

S202, for the roll angle ϕ(t), in order to reach a target angle ϕ_(T)(t), first defining an error function e_(ϕ1)=ϕ(t)−ϕ_(T)(t), such that we can obtain e_(ϕ1)={dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t); since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(ϕ1)(t)=γ(t)Φ(e_(ϕ1) (t),t),

${{\Phi\left( {{e_{\phi 1}(t)},t} \right)} = {{k_{1}{{e_{\phi 1}(t)}}^{r}{sign}\;\left( {e_{\phi 1}(t)} \right)} + {k_{2}{e_{\phi 1}(t)}} + {k_{3}{{e_{\phi 1}(t)}}^{\frac{1}{r}}{sign}\;\left( {e_{\phi 1}(t)} \right)}}};$

by substituting the error function e_(ϕ1)(t)=ϕ(t)−ϕ_(T)(t) and ė_(ϕ1)={dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t) into the equation ė_(ϕ1)(t)=−γ(t)Φ(e_(ϕ1)(t),t), we can obtain

{dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(t ^(p) +p)Φ(e _(ϕ1)(t),t=0,   (7)

ϕ(t) will converge to the target angle ϕ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (ϕ)}(t) is known, it is necessary to solve the equation involving {umlaut over (ϕ)}(t); in order to obtain the equation involving {umlaut over (ϕ)}(t), the error function e_(ϕ2)={dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(t^(p)+p)Φ(e_(ϕ1) (t),t) is set by the same method and ė_(ϕ2) (t)={umlaut over (ϕ)}(t)−{umlaut over (ϕ)}_(T)(t)+(p+t^(p)){dot over (Φ)}(e_(ϕ1)(t),t)+pt^(p−1)Φ(e_(ϕ1)(t),t),

${{\Phi\left( {{e_{\phi 2}(t)},t} \right)} = \left. k_{1} \middle| {e_{\phi 2}(t)} \middle| {}_{r}{{{sign}\;\left( {e_{\phi 2}(t)} \right)} + {k_{2}{e_{\phi 2}(t)}} + k_{3}} \middle| {e_{\phi 2}(t)} \middle| {}_{\frac{1}{r}}{{sign}\;\left( {e_{\phi 2}(t)} \right)} \right.};$

by substituting the above equations of e_(ϕ2)(t) and ė_(ϕ2)(t) into the equation ė_(φ2)(t)=−γ(t)Φ(e_(ϕ2) (t),t), the following function can be obtained:

{umlaut over (ϕ)}(t)−{umlaut over (ϕ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ϕi)(t),t)+Φ(e _(ϕ2)(t),t)+pt ^(p−1)Φ(e _(ϕ1)(t),t)=0   (8)

when equation (8) is established, the velocity layer {dot over (ϕ)}(t) will converge to {dot over (ϕ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered

E _(ϕ)={umlaut over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ϕi)(t),t)+Φ(e _(ϕ2)(t),t)+pt ^(p−1)Φ(e _(ϕi)(t),t)   (9)

when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into

$\begin{matrix} {{{E_{\phi}(t)} = {{\frac{l}{J_{ϰ}}{u_{2}(t)}} + {b_{\phi}(t)}}},} & (10) \end{matrix}$

wherein

${b_{\phi}(t)} = {\frac{\left( {J_{y} - J_{z}} \right){\overset{.}{\psi}(t)}{\overset{.}{\theta}(t)}}{J_{x}} - {{\overset{¨}{\phi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\phi 1}(t)},t} \right)}} + {pt^{p - 1}{\Phi\left( {{e_{\phi 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\phi 2}(t)},t} \right)} \right)}}$

that is, the deviation function about the output control parameter u₂(t) is obtained;

S203, for the pitch angle θ(t), in order to reach a target angle θ_(T) (t), first defining an error function e_(θ1)=θ(t)−θ_(T)(t), such that we can obtain ė_(θ1)={dot over (θ)}(t)−{dot over (θ)}_(T)(t), since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(θ1)(t)=−γ(t)Φ(e_(θ1)(t),t)

${{\Phi\left( {{e_{\theta 1}(t)},t} \right)} = \left. k_{1} \middle| {e_{\theta 1}(t)} \middle| {}_{r}{{{sign}\;\left( {e_{\theta 1}(t)} \right)} + {k_{2}{e_{\theta 1}(t)}} + k_{3}} \middle| {e_{\theta 1}(t)} \middle| {}_{\frac{1}{r}}{{sign}\;\left( {e_{\theta 1}(t)} \right)} \right.};$

by substituting the error function e_(θ1)(t) and ė_(θ1) into the equation ė_(e1)(t)=−γ(t)Φ(e_(θ1)(t),t), we can obtain

{dot over (θ)}(t)−{dot over (θ)}_(T)(t)+(t ^(p) +p)Φ(e _(θ1)(t),t)=0,   (11)

θ(t) will converge to the target angle θ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (θ)}(t) is known, it is necessary to solve the equation involving {umlaut over (θ)}(t); in order to obtain the equation involving {umlaut over (θ)}(t), the error function e_(θ2)={dot over (θ)}(t)−{dot over (θ)}_(T)(t)+(t^(p)+p)Φ(e_(θ1) (t),t) is set by the same method and ė_(θ2)={umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t^(p)){dot over (Φ)}(e_(θ1) (t),t)+pt^(p−1)Φ(e_(θ1)(t),t),

${{\Phi\left( {{e_{\theta 2}(t)},t} \right)} = \left. k_{1} \middle| {e_{\theta 2}(t)} \middle| {}_{r}{{{sign}\;\left( {e_{\theta 2}(t)} \right)} + {k_{2}{e_{\theta 2}(t)}} + k_{3}} \middle| {e_{\theta 2}(t)} \middle| {}_{\frac{1}{r}}{{sign}\;\left( {e_{\theta 2}(t)} \right)} \right.};$

by substituting the above equations of e_(θ2)(t) and ė_(θ2)(t) into ė_(φ2)(t)=−γ(t)Φ(e_(φ2)(t),t), the following function can be obtained:

{umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(θi)(t),t)+Φ(e _(θ2)(t),t)+pt ^(p−1)Φ(e _(θ1)(t),t)=0   (12)

when equation (12) is established, the velocity layer {dot over (θ)}(t) will converge to {dot over (θ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered

E _(θ)(t)={umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(θ1)(t),t)+Φ(e _(θ2)(t),t)+pt ^(p−1)Φ(e _(θ1) ,t),t)   (13)

when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into

$\begin{matrix} {{{E_{\theta}(t)} = {{\frac{l}{J_{y}}{u_{3}(t)}} + {b_{\theta}(t)}}},} & (14) \end{matrix}$

wherein

${{b_{\theta}(t)} = {\frac{\left( {J_{z} - J_{ϰ}} \right){\overset{.}{\psi}(t)}\overset{.}{\phi}(t)}{J_{y}} - {{\overset{¨}{\phi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\theta 1}(t)},t} \right)}} + {pt^{p - 1}{\Phi\left( {{e_{\theta 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\theta 1}(t)},t} \right)} \right)}}},$

that is, the deviation function about the output control parameter u₃(t) is obtained;

and

S204, for the yaw angle ψ(t), in order to reach a target angle ψ_(T)(t), first defining an error function e_(ψ1)=ψ(t)−ψ_(T)(t), such that we can obtain ė_(ψ1)={dot over (ψ)}(t)−{dot over (ψ)}_(T) (t), since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(ψ1)(t)=−γ(t)Φ(e_(ψ1)(t),t)

${{\Phi\left( {{e_{\psi 1}(t)},t} \right)} = \left. k_{1} \middle| {e_{\psi 1}(t)} \middle| {}_{r}{{{sign}\;\left( {e_{\psi 1}(t)} \right)} + {k_{2}{e_{\psi 1}(t)}} + k_{3}} \middle| {e_{\psi 1}(t)} \middle| {}_{\frac{1}{r}}{{sign}\;\left( {e_{\psi 1}(t)} \right)} \right.};$

by substituting the error function e_(ψ1)(t) and ė_(ψ1)(t) into the equation ė_(ψ1) (t)=−γ(t)Φ(e_(ψ1)(t),t), we can obtain

{dot over (ψ)}(t)−{dot over (ψ)}(t)+(t ^(p) +p)Φ(e _(ψ1)(t),t)=0,  (15)

ψ(t) will converge to the target angle ψ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (ψ)}(t) is known, it is necessary to solve the equation involving {umlaut over (ψ)}(t); in order to obtain the equation involving {umlaut over (ψ)}(t), the error function e_(ψ2)={dot over (ψ)}(t)−{dot over (ψ)}_(T)(t)+(t^(p)+p)Φ(e_(ψ1) (t),t) is set by the same method and

${{{\overset{.}{e}}_{\psi 2}(t)} = {{\overset{¨}{\psi}(t)} - {{\overset{¨}{\psi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\psi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\psi 1}(t)},t} \right)}}}},{{{\Phi\left( {{e_{\psi 2}(t)},t} \right)} = {{k_{1}{{e_{\psi 2}(t)}}^{r}{{sign}\left( {e_{\psi 2}(t)} \right)}} + {k_{2}{e_{\psi 2}(t)}} + {k_{3}{{e_{\psi 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\psi 2}(t)} \right)}}}};}$

by substituting the above equations of e_(ψ2)(t) and ė_(ψ2)(t) into ė_(φ2) (t)=−γ(t)Φ(e_(φ2)(t),t) the following function can be obtained:

{umlaut over (ψ)}(t)−{umlaut over (ψ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ψ1)(t),t)+Φ(e _(ψ2)(t),t)+pt ^(p−1)101(e _(ψ1)(t),t=0   (16)

when equation (16) is established, the velocity layer {dot over (ψ)}(t) will converge to {dot over (ψ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered

E _(ψ)(t)={umlaut over (ψ)}(t)−{umlaut over (ψ)}T(t)+(p+t ^(p)){dot over (Φ)}(e _(ψ1)(t),t)+Φ(e _(ψ2)(t),t)+pt ^(p−1)Φ(e _(ψ1)(t),t)   (17)

when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into

$\begin{matrix} {{{E_{\psi}(t)} = {{\frac{1}{J_{z}}{u_{4}(t)}} + {b_{\psi}(t)}}},} & (18) \end{matrix}$

wherein

${{b_{\psi}(t)} = {\frac{\left( {J_{x} - J_{y}} \right){\overset{.}{\phi}(t)}{\overset{.}{\theta}(t)}}{J_{z}} - {{\overset{¨}{\psi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\psi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\psi 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\psi 2}(t)},t} \right)} \right)}}},$

that is, the deviation function about the output control parameter u₄(t) is obtained;

Further, the step of designing the finite-time varying-parameter convergence differential neural network solver according to the obtained system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄, respectively, specifically comprises:

S211, for the z-axis height z(t), by using the finite-time varying-parameter convergence differential neural network design method, designing Ė_(z) (t)=γ(t)Φ(E_(z)(t),t) and substituting equation (6) and the derivative Ė_(z)(t)={dot over (a)}_(z) (t)u₁(t)+a_(z)(t){dot over (u)}₁(t)+{dot over (b)}_(z)(t) so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

a _(z)(t){dot over (u)} ₁(t)=−({dot over (a)} _(z)(t)u ₁(t)+{dot over (b)} _(z)(t)+y(t)Φ(E _(z)(t),t))  (19)

the position z(t) and velocity z(t) will converge to a target position z_(T)(t) and a target velocity ż_(T)(t), respectively, in a super-exponential manner within finite time;

S212, for the roll angle ϕ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(ϕ)(t)=−γ(t)Φ(E_(ϕ)(t),t), and substituting equation (10) and its derivative

${{{\overset{.}{E}}_{\phi}(t)} = {{\frac{l}{J_{x}}{{\overset{.}{u}}_{1}(t)}} + {{\overset{.}{b}}_{\phi}(t)}}},$

so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

$\begin{matrix} {{\frac{l}{J_{x}}{{\overset{.}{u}}_{2}(t)}} = {- \left( {{{\overset{.}{b}}_{\phi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\phi}(t)},t} \right)}}} \right)}} & (20) \end{matrix}$

the roll angle ϕ(t) and velocity {dot over (ϕ)}(t) will converge to a target position ϕ_(T)(t) and a target velocity {dot over (ϕ)}_(T)(t), respectively, in a super-exponential manner within finite time;

S213, for the pitch angle θ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(θ)(t)=−γ(t)Φ(E_(θ)(t) t), and substituting equation (14) and its derivative

${{{\overset{.}{E}}_{\theta}(t)} = {{\frac{l}{J_{x}}{{\overset{.}{u}}_{3}(t)}} + {{\overset{.}{b}}_{\theta}(t)}}},$

so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

$\begin{matrix} {{\frac{l}{J_{y}}{{\overset{.}{u}}_{3}(t)}} = {- \left( {{{\overset{.}{b}}_{\theta}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\theta}(t)},t} \right)}}} \right)}} & (21) \end{matrix}$

the pitch angle θ(t) and velocity {dot over (ϕ)}(t) will converge to a target position θ_(T)(t) and a target velocity {dot over (θ)}_(T)(t), respectively, in a super-exponential manner within finite time;

S214, for the yaw angle ψ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(ψ)(t)=−γ(t)Φ(E_(ψ)(t),t), and substituting equation (18) and its derivative

${{{\overset{.}{E}}_{\psi}(t)} = {{\frac{l}{J_{z}}{{\overset{.}{u}}_{4}(t)}} + {{\overset{.}{b}}_{\psi}(t)}}},$

so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

$\begin{matrix} {{\frac{l}{J_{z}}{{\overset{.}{u}}_{4}(t)}} = {- \left( {{{\overset{.}{b}}_{\psi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\psi}(t)},t} \right)}}} \right)}} & (22) \end{matrix}$

the pitch angle ψ(t) and velocity {dot over (ψ)}(t) will converge to a target position ψ_(T)(t) and a target velocity {dot over (ψ)}_(T)(t), respectively, in a super-exponential manner within finite time; and

S215, solving the synthesized control parameters u₁˜u₄ which is the control parameters corresponding to the flight demand of the aerial vehicle, according to equations (19), (20), (21) and (22), obtaining the neural network equations of the control parameters u₁˜u₄ respectively as follows:

$\begin{matrix} \left\{ \begin{matrix} {{{\overset{.}{u}}_{1}(t)} = \frac{- \left( {{{{\overset{.}{a}}_{z}(t)}{u_{1}(t)}} + {{\overset{.}{b}}_{z}(t)} + {{\gamma\Phi}\left( {{E_{z}(t)},t} \right)}} \right)}{a_{z}(t)}} \\ {{\overset{.}{u}}_{2} = {{- \left( {{b_{\phi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\phi}(t)},t} \right)}}} \right)}\frac{J_{x}}{l}}} \\ {{\overset{.}{u}}_{3} = {{- \left( {{b_{\theta}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\theta}(t)},t} \right)}}} \right)}\frac{J_{y}}{l}}} \\ {{\overset{.}{u}}_{4} = {{- \left( {{b_{\psi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\psi}(t)},t} \right)}}} \right)}J_{z}}} \end{matrix} \right. & (23) \end{matrix}$

and performing different output control assignments with the solved control parameters u₁˜u₄ according to the structure of and the number of motors of different rotor aerial vehicles.

Compared with the prior art, the invention has the advantages and effects as follows.

The present invention is based on the varying-parameter convergence differential neurodynamics method, is described by using a ubiquitous implicit dynamics model, can fully utilize derivative information of various time-varying parameters from a method and system level, has a certain predictive capability for solving problems, can approximate the correct solution of the problem in a quick, accurate and real-time way, and can well solve a variety of time-varying problems such as matrix, vector, algebra and optimization.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a flow chart of a stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics disclosed by the invention;

FIG. 2 is a side view showing the structure of the multi-rotor aerial vehicle of the invention;

FIG. 3 is a top view showing the structure of the multi-rotor aerial vehicle of the invention;

FIG. 4 is a three-dimensional view showing the structure of the multi-rotor aerial vehicle of the invention; and

FIG. 5 is a diagram showing a body coordinate system of the multi-rotor aerial vehicle.

DETAILED DESCRIPTION OF EMBODIMENTS

In order to make the objectives, technical solutions and advantages of embodiments of the invention clearer, the technical solutions in embodiments of the invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the invention. Apparently, the described embodiments are a part, but not all of the embodiments of the invention. Based on the embodiments of the invention, all other embodiments obtained by those of ordinary skill in the art without involving any inventive effort fall within the scope of protection of the invention.

EMBODIMENTS

FIG. 1 is a flow chart of a stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics disclosed by the invention. The design of a neural network controller for an aerial vehicle can be achieved through the steps shown in the figure:

As shown in the figure, a stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics comprises the steps of:

S1, acquiring real-time flight operation data of a multi-rotor unmanned aerial vehicle through an airborne attitude sensor and corresponding height and position sensors thereof, establishing a dynamics model of the aerial vehicle, and analyzing and processing kinematic problems of the aerial vehicle correspondingly through a processor borne by the multi-rotor unmanned aerial vehicle;

S2, designing a finite-time varying-parameter convergence differential neural network solver for the dynamics model of the multi-rotor aerial vehicle according to a finite-time varying-parameter convergence differential neurodynamics design method;

S3, solving output control parameters of motors of the aerial vehicle, through the finite-time varying-parameter convergence differential neural network solver designed in step S2 and using the real-time operation data and target attitude data of the aerial vehicle acquired in step S1; and

S4, transmitting results of step S3 to speed regulators of the motors of the aerial vehicle to control the motion of the multi-rotor unmanned aerial vehicle.

The mechanism shown in FIGS. 2, 3 and 4 is a rotor aerial vehicle structure of multi-rotor aerial vehicles. The structure is a six-rotor aerial vehicle mechanism model, which consists of multi-rotor aerial vehicle propellers 1, brushless motors 2, rotor arms 3 and a body 4. The output resultant force of the six motors and the synthesized rotational torque constitute the control parameters u₁˜u₄ of the multi-rotor aerial vehicle. However, the control design of the invention lies in solving the control parameters of the multi-rotor aerial vehicle through the designed finite-time varying-parameter convergence differential neural network, thereby controlling the flight of the aerial vehicle and realizing the stability control of the aerial vehicle. The directions of rotation arrows in FIGS. 3 and 4 indicate the directions of rotation of the motors, and the combination of the illustrated clockwise and counterclockwise directions of rotation is to achieve mutual offsetting of torques of the motors so as to achieve stable steering control.

FIG. 5 is a schematic diagram of a body coordinate system of the multi-rotor aerial vehicle. According to the body coordinate system, the following definitions are given:

(1) six motors of the six-rotor aerial vehicle are defined No. 1 to No. 6 in the clockwise direction;

(2) the x-axis extends in the direction of No. 1 rotor arm and points to the forward direction of the aerial vehicle through the center of gravity of the body;

(3) the y-axis extends in the direction of the axis of symmetry of No. 2 and No. 3 rotor arms and points to the right motion direction of the aerial vehicle through the center of gravity of the body;

(4) the z-axis extends upwardly perpendicular to the plane of the six rotors and points to the climbing direction of the aerial vehicle through the center of gravity of the body;

(5) the pitch angle θ(t) is an included angle between the x-axis of the body and the geodetic horizontal plane, and is set to be positive in the downward direction;

(6) the roll angle ϕ(t) is an included angle between the z-axis of the body and the geodetic vertical plane passing through the x-axis of the body, and is set to be positive when the body is rightward; and

(7) the yaw angle ψ(t) is an included angle between the projection of the x-axis of the body on the geodetic horizontal plane and the x-axis of a geodetic coordinate system, and is set to be positive when the nose of the aerial vehicle is leftward.

According to the relevant steps of the flow chart, detailed algorithm analysis is carried out for the invention. First, with the above definition of the attitude variables of the aerial vehicle, real-time attitude data θ(t), ϕ(t) and ψ(t) of the aerial vehicle may be acquired by sensors such as gyros and accelerometers borne by the multi-rotor aerial vehicle by means of quaternion algebra, Kalman filtering and other algorithms, and position data x(t), y(t) and z(t) of the aerial vehicle in the three-dimensional space is acquired by using altitude sensors and position sensors. The above completes the relevant contents of data acquisition 1 by the sensors in the flow chart.

Based on the previous physical model analysis process, according to different rotor aerial vehicle models, physical model equations and dynamics equations for the aerial vehicle are established, and dynamics analysis may be completed by means of the following aerial vehicle dynamics modeling steps:

ignoring the effect of air resistance on the aerial vehicle, such that a physical model can be established for the aerial vehicle system:

$\begin{matrix} {{{{\begin{bmatrix} {mI} & 0_{3 \times 3} \\ 0_{3 \times 3} & J \end{bmatrix}\begin{bmatrix} \overset{.}{v} \\ \overset{.}{w} \end{bmatrix}} + \begin{bmatrix} {w \times ({mv})} \\ {w \times ({Jw})} \end{bmatrix}} = {\begin{bmatrix} F \\ T \end{bmatrix} + \begin{bmatrix} G \\ 0_{3 \times 3} \end{bmatrix}}},} & (1) \end{matrix}$

wherein m is a total mass of the aerial vehicle, I is a 3×3 identity matrix, J is a rotational inertia matrix of the aerial vehicle, v and w are a velocity vector and an angular velocity vector of the aerial vehicle in a ground coordinate system, F and G are an axial component vector of an output resultant force of the motors of the aerial vehicle and an axial component vector of gravity of the aerial vehicle, respectively, and T is a rotational torque vector of the aerial vehicle;

establishing a ground coordinate system X_(G) and an aerial vehicle body coordinate system X_(U), wherein the ground coordinate system and the body coordinate system have the following relationship: X_(U)=KX_(G), in which conversion relationship, K is a rotation conversion matrix between the ground coordinate system and the body coordinate system, which can be expressed as

${K = \begin{bmatrix} {C_{\theta}C_{\psi}} & {C_{\theta}S_{\psi}} & {- S_{\theta}} \\ {S_{\phi}S_{\theta}C_{\psi}} & {{S_{\phi}S_{\theta}S_{\psi}} + {C_{\phi}S_{\psi}}} & {S_{\phi}C_{\theta}} \\ {{S_{\phi}S_{\theta}C_{\psi}} - {C_{\phi}S_{\psi}}} & {{C_{\phi}S_{\theta}S_{\psi}} - {S_{\theta}C_{\psi}}} & {C_{\theta}C_{\phi}} \end{bmatrix}},$

wherein, for the convenience of writing, C_(θ) represents cos θ(t) S_(θ) represents sin θ(t), θ(t) is the pitch angle, ψ(t) is the yaw angle, and ϕ(t) is the roll angle;

according to the coordinate conversion theory, in a translation direction and a rotation direction of the aerial vehicle, basing on the above physical model, such that the following dynamics equation in the aerial vehicle body coordinate system can be obtained

$\begin{matrix} \left\{ {\begin{matrix} {\overset{¨}{x} = \frac{{u_{1}(t)}\left( {{\cos\;{\phi(t)}\sin\;{\theta(t)}\cos\;{\psi(t)}} + {\sin\;{\theta(t)}\sin\;{\psi(t)}}} \right)}{m}} \\ {\overset{¨}{y} = \frac{{u_{1}(t)}\left( {{\sin\;{\phi(t)}\sin\;{\theta(t)}\cos\;{\psi(t)}} - {\sin\;{\psi(t)}\cos\;{\psi(t)}}} \right)}{m}} \\ {\overset{¨}{z} = {\frac{{u_{1}(t)}\cos\;{\theta(t)}\cos\;{\phi(t)}}{m} - g}} \\ {\overset{¨}{\phi} = \frac{{l \cdot {u_{2}(t)}} + {\left( {J_{y} - J_{z}} \right){\overset{.}{\psi}(t)}{\overset{.}{\theta}(t)}}}{J_{y}}} \\ {\overset{¨}{\theta} = \frac{{l \cdot {u_{3}(t)}} + {\left( {J_{z} - J_{x}} \right){\overset{.}{\psi}(t)}{\overset{.}{\phi}(t)}}}{J_{y}}} \\ {\overset{¨}{\psi} = \frac{{u_{4}(t)} + {\left( {J_{x} - J_{y}} \right){\overset{.}{\theta}(t)}{\overset{.}{\phi}(t)}}}{J_{z}}} \end{matrix},} \right. & (2) \end{matrix}$

wherein x, y, z are position coordinates of the aerial vehicle in the world coordinate system, respectively; J_(x), J_(Y) and J_(z) are rotational inertia of the aerial vehicle in x-axis, Y-axis and z-axis directions, respectively; l is an arm length; g is gravitational acceleration; synthesized control parameters u₁˜u₄ consist of output thrust of the motors of the aerial vehicle and a synthesized torque, u₁(t) is a resultant force in a vertical ascending direction of the aerial vehicle, u₂ (t) is a resultant force in a roll angle direction, u₃(t) is a resultant force in a pitch angle direction, and u₄(t) is the synthesized torque in a yaw angle direction.

The designing a finite-time varying-parameter convergence differential neural network solver for the dynamics model of the multi-rotor aerial vehicle according to a finite-time varying-parameter convergence differential neurodynamics design method of step S2 specifically comprises:

by means of the finite-time varying-parameter convergence differential neurodynamics design method, designing a system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄ in respect to the z-axis height z(t), the roll angle ϕ(t), the pitch angle θ(t) and the yaw angle ψ(t), respectively; and

designing the finite-time varying-parameter convergence differential neural network solver according to the obtained system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄, respectively.

In step S3, the step of by means of the finite-time varying-parameter convergence differential neurodynamics design method, designing a system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄ in respect to the z-axis height z(t), the roll angle ϕ(t), the pitch angle θ(t) and the yaw angle ψ(t), respectively, specific ally comprises:

for the z-axis height z(t), according to a set target height value and an actual height value z_(T)(t) in the z-axis direction, defining a deviation function e_(z1) about the actual height value z(t) on a position layer as follows: e_(z1)(t)=z(t)−z_(T)(t), in order to enable the actual value z(t) to converge to the time-varying target value z_(T)(t), designing a neurodynamics equation ė_(z1)(t)=−γ(t)Φ(e_(z1)(t),t) based on a deviation function according to the finite-time varying-parameter convergence differential neurodynamics design method, wherein γ(t)=p+t^(p) is a time-varying parameter representing a regulatory factor for the rate of convergence;

${\overset{.}{\Phi}\left( {{e_{z\; 1}(t)},t} \right)} = {{k_{1}{{e_{z\; 1}(t)}}^{r}{{sign}\left( {e_{z\; 1}(t)} \right)}} + {k_{2}{e_{z\; 1}(t)}} + {k_{3}{{e_{z\; 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{z\; 1}(t)} \right)}}}$

according to the deviation function e_(z1)(t)=z(t)−z_(T) (t), ė_(z1)=ż(t)−ż_(T) (t) can be obtained; by substituting e_(z1)(t)=z(t)−z_(T) (t) and ė_(z1)=ż(t)−ż_(T)(t) into ė_(z1)(t)=−γ(t)Φ(e_(z1)(t),t), we can obtain ż(t)−ż_(T)(t)=−(t^(p)+p)Φ(e_(z1)(t),t), that is

ż(t)−ż _(T)(t)+(t ^(p) +p)Φ(e _(z1)(t),t)=0;  (3)

the position layer z(t) can converge to the time-varying target value z_(T)(t) in a super-exponential manner within a finite time, however, since equation (3) does not contain relevant information about the control parameters u₁˜u₄, the solution of the control parameters cannot be realized, therefore, it is necessary to further design the deviation function including a velocity layer ż(t) and an acceleration layer {umlaut over (z)}(t), thus defining e_(z2) (t)=ż(t)−ż_(T)(t^(p)+p)Φ(e_(z1) (t),t); according to the finite-time varying-parameter convergence differential neural network design method, the dynamics equation ė_(z2)(t)=−γ(t)Φ(e_(z2)(t),t) based on the deviation function can be designed,

${\Phi\left( {{e_{z\; 2}(t)},t} \right)} = {{k_{1}{{e_{z\; 2}(t)}}^{r}{{sign}\left( {e_{z\; 2}(t)} \right)}} + {k_{2}{e_{z\; 2}(t)}} + {k_{3}{{e_{z\; 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{z\; 2}(t)} \right)}}}$

according to e_(z2)(t)=ż(t)−ż_(T)(t) (t^(p)+p)Φ(e_(z1) (t),t) the derivative ė_(z2) (t) of the deviation function e_(z2)(t) is known as: ė_(z2) (t)={umlaut over (z)}_(T) (t) (p+t^(p)){dot over (Φ)}(e_(z1)(t),t)+pt^(p−1)Φ(e_(z1)(t),t) by substituting the above equations about e_(z2) (t) and ė_(z2)(t) into the equation the ė_(φ2)(t)=−γ(t)Φ(e_(φ2)(t),t), the following function can be obtained:

{umlaut over (z)}(t)−{umlaut over (z)} _(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(z1)(t),t)+Φ(e _(z2)(t),t)+pt ^(p−1)Φ(e _(z1)(t),t)=0  (4)

when equation (4) is established, the velocity layer ż(t) will converge to ż_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered

E _(z)(t)={umlaut over (z)}(t)−{umlaut over (z)} _(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(z1)(t),t)+Φ(e _(z2)(t),t)+pt ^(p−1)Φ(e _(z1)(t),t)   (5)

in order to obtain an actual model of the neural network, in combination with kinetic equation (2), equation (5) can be rewritten into

E _(z)(t)=a _(z)(t)tt _(i)(t)+b _(z)(t)  (6)

wherein

${{a_{z}(t)} = \frac{\cos\mspace{14mu}{\theta(t)}\mspace{14mu}\cos\mspace{14mu}{\phi(t)}}{m}},$

b_(z)=g−{umlaut over (z)}_(T)(t)+(p+t^(p)){dot over (Φ)}(e_(z1)(t),t)+pt^(p−1)Φ(e_(z1)(t),t)+(p+t^(p))Φ(e_(z2)(t),t) that is, the deviation function about the output control parameter u₁(t) is obtained;

for the roll angle ϕ(t), in order to reach a target angle ϕ_(T)(t), first defining an error function e_(ϕ1)=ϕ(t)−ϕ_(T)(t), such that we can obtain ė_(ϕ1)={dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t); since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(ϕ1)(t)=−γ(t)Φ(e_(ϕ1)(t),t),

${{\Phi\left( {{e_{\phi 1}(t)},t} \right)} = {{k_{1}{{e_{\phi 1}(t)}}^{r}{{sign}\left( {e_{\phi 1}(t)} \right)}} + {k_{2}{e_{\phi 1}(t)}} + {k_{3}{{e_{\phi 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\phi 1}(t)} \right)}}}};$

by substituting the error function e_(ϕ1)(t) and ė_(ϕ1)(t) into the equation ė_(ϕ1)(t)=−γ(t)Φ(e_(ϕ1)(t),t) we can obtain

{dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(t ^(p) +p)Φ(e _(ϕ1)(t),t)=0,  (7)

ϕ(t) will converge to the target angle ϕ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (ϕ)}(t) is known, it is necessary to solve the equation involving {umlaut over (ϕ)}(t); in order to obtain the equation involving {umlaut over (ϕ)}(t), the error function e_(ϕ2)={dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(t^(p)+p)Φ(e_(ϕ1)(t),t) is set by the same method and ė_(ϕ2)(t)={umlaut over (ϕ)}(t)−{umlaut over (ϕ)}_(T)(t)+(p+t^(p)){dot over (Φ)}(e_(ϕ1)(t),t)+pt^(p−1)Φ(e_(ϕ1)(t),t),

${{\Phi\left( {{e_{\phi 2}(t)},t} \right)} = {{k_{1}{{e_{\phi 2}(t)}}^{r}{{sign}\left( {e_{\phi 2}(t)} \right)}} + {k_{2}{e_{\phi 2}(t)}} + {k_{3}{{e_{\phi 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\phi 2}(t)} \right)}}}};$

by substituting the above equations of e_(ϕ2)(t) and ė_(ϕ2)(t) into ė_(φ2) (t)=−γ(t)Φ(e_(φ2)(t),t), the following function can be obtained:

{umlaut over (ϕ)}(t)−{umlaut over (ϕ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ϕ1)(t),t)+Φ(e _(ϕ2)(t),t)+pt ^(p−1)Φ(e _(ϕ1)(t),t)=0   (8)

when equation (8) is established, the velocity layer {dot over (ϕ)}(t) will converge to {dot over (ϕ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered

E _(ϕ)={umlaut over (ϕ)}(t)−{umlaut over (ϕ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ϕ1)(t),t)+Φ(e _(ϕ2)(t),t)+pt ^(p−1)Φ(e _(ϕ1)(t),t)   (9)

when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into

$\begin{matrix} {{E_{\phi}(t)} = {{\frac{l}{J_{x}}{u_{2}(t)}} + {b_{\phi}(t)}}} & (10) \end{matrix}$

wherein

${{b_{\phi}(t)} = {\frac{\left( {J_{y} - J_{z}} \right){\overset{.}{\psi}(t)}{\overset{.}{\theta}(t)}}{J_{x}} - {{\overset{¨}{\phi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\phi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\phi 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\phi 2}(t)},t} \right)} \right)}}},$

that is, the deviation function about the output control parameter u₂(t) is obtained;

for the pitch angle θ(t), in order to reach a target angle θ_(T)(t), first defining an error function e_(θ1)=θ(t)−θ_(T)(t), such that we can obtain ė_(θ1)={dot over (θ)}(t)−{dot over (θ)}_(T)(t); since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(θ1)(t)=γ(t)Φ(e_(θ1)(t),t),

${{\Phi\left( {{e_{\theta 1}(t)},t} \right)} = {{k_{1}{{e_{\theta 1}(t)}}^{r}{{sign}\left( {e_{\theta 1}(t)} \right)}} + {k_{2}{e_{\theta 1}(t)}} + {k_{3}{{e_{\theta 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\theta 1}(t)} \right)}}}};$

by substituting the error function e_(θ1)(t) and ė_(θ1)(t) into the equation ė_(θ1)(t)=−γ(t)Φ(e_(θ1)(t),t), we can obtain

{dot over (θ)}(t)−{dot over (θ)}_(T)(t)+(t ^(p) +p)Φ(e _(θ1)(t),t)=0,  (11)

θ(t) will converge to the target angle θ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (θ)}(t) is known, it is necessary to solve the equation involving {umlaut over (θ)}(t); in order to obtain the equation involving {umlaut over (θ)}(t), the error function e_(θ2)={dot over (θ)}(t)−{dot over (θ)}_(T) (t)+(t^(p)+p)Φ(e_(θ1)(t),t) is set by the same method

and ė_(θ2) (t)={umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t^(p))(e_(θ1)(t),t)+pt^(p−1)Φ(e_(θ1)(t),t)

${{\Phi\left( {{e_{\theta 2}(t)},t} \right)} = {{k_{1}{{e_{\theta 2}(t)}}^{r}{{sign}\left( {e_{\theta 2}(t)} \right)}} + {k_{2}{e_{\theta 2}(t)}} + {k_{3}{{e_{\theta 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\theta 2}(t)} \right)}}}};$

by substituting the above equations of e_(θ2)(t) and ė_(θ2)(t) into ė_(φ2) (t)=−γ(t)Φ(e_(φ2)(t),t), the following function can be obtained:

{umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(θ1)(t),t)+Φ(e _(θ2)(t),t)+pt ^(p−1)Φ(e _(θ1)(t),t)=0   (12)

when equation (12) is established, {dot over (θ)}(t) will converge to {dot over (θ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function is considered

E _(θ)(t)={umlaut over (θ)}(t)+{umlaut over (θ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(θ1)(t),t)Φ(e _(θ2)(t),t)+pt ^(p−1)Φ(e _(θ1)(t),t)   (13)

when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into

$\begin{matrix} {{{E_{\theta}(t)} = {{\frac{l}{J_{y}}{u_{3}(t)}} + {b_{\theta}(t)}}},} & (14) \end{matrix}$

wherein

${{b_{\theta}(t)} = {\frac{\left( {J_{z} - J_{x}} \right){\overset{.}{\psi}(t)}{\overset{.}{\theta}(t)}}{J_{y}} - {{\overset{¨}{\phi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\theta 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\theta 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\theta 2}(t)},t} \right)} \right)}}},$

that is, the deviation function about the output control parameter u₃(t) is obtained;

for the yaw angle ψ(t), in order to reach a target angle ψ_(T)(t), first defining an error function e_(ψ1)=ψ(t)−ψ_(T)(t), such that we can obtain ė_(ψ1)={dot over (ψ)}(t)−{dot over (ψ)}_(T)(t); since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(ψ1)(t)=−γ(t)Φ(e_(ψ1) (t),t)

${{\Phi\left( {{e_{\psi 1}(t)},t} \right)} = {{k_{1}{{e_{\psi 1}(t)}}^{r}{{sign}\left( {e_{\psi 1}(t)} \right)}} + {k_{2}{e_{\psi 1}(t)}} + {k_{3}{{e_{\psi 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\psi 1}(t)} \right)}}}};$

by substituting the error function e_(ψ1)(t) and ė_(ψ1)(t) into the equation ė_(ψ1) (t)=−γ(t)Φ(e_(ψ1)(t),t) we can obtain

{dot over (ψ)}(t)−ψ_(T)(t)+(t ^(p) +p)Φ(e _(ψ1)(t),t)=0,   (15)

ψ(t) will converge to the target angle ψ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (ψ)}(t) is known, it is necessary to solve the equation involving {umlaut over (ψ)}(t); in order to obtain the equation involving {umlaut over (ψ)}(t), the error function e_(ψ2)={dot over (ψ)}(t)−{dot over (ψ)}_(T)(t)+(t^(p)+p)Φ(e_(ψ1)(t),t) is set by the same method and

${{\overset{.}{e}}_{\psi 2} = {{\overset{¨}{\psi}(t)} - {{\overset{¨}{\psi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\psi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\psi 1}(t)},t} \right)}}}},{{{\Phi\left( {{e_{\psi 2}(t)},t} \right)} = {{k_{1}{{e_{\psi 2}(t)}}^{r}{{sign}\left( {e_{\psi 2}(t)} \right)}} + {k_{2}{e_{\psi 2}(t)}} + {k_{3}{{e_{\psi 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\psi 2}(t)} \right)}}}};}$

by substituting the above equations of e_(ψ2)(t) and ė_(ψ2)(t) into ė_(φ2)(t)=−γ(t)Φ(e_(φ2)(t),t), the following function can be obtained:

{umlaut over (ψ)}(t)−{umlaut over (ψ)}(t)+(p+t ^(p))Φ(e _(ψ1)(t),t)+Φ(e _(ψ2)(t),t)±pt ^(p−1)Φ(e _(ψ1)(t),t)=0   (16)

when equation (16) is established, the velocity layer {dot over (ψ)}(t) will converge to {dot over (ψ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered

E _(ψ)(t)={umlaut over (ψ)}(t)−{umlaut over (ψ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ψ1)(t),t)+Φ(e _(ψ2)(t),t)+pt ^(p−1)Φ(e _(ψ)(t),t)   (17)

when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into

$\begin{matrix} {{{E_{\psi}(t)} = {{\frac{1}{J_{z}}{u_{4}(t)}} + {b_{\psi}(t)}}},} & (18) \end{matrix}$

wherein

${{b_{\psi}(t)} = {\frac{\left( {J_{x} - J_{y}} \right){\overset{.}{\phi}(t)}{\overset{.}{\theta}(t)}}{J_{z}} - {{\overset{¨}{\psi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\psi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\psi 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\psi 2}(t)},t} \right)} \right)}}},$

that is, the deviation function about the output control parameter u₄(t) is obtained;

wherein, in step S4, the step of designing the finite-time varying-parameter convergence differential neural network solver according to the obtained system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄, respectively, specifically comprises:

for the z-axis height z(t), by using the finite-time varying-parameter convergence differential neural network design method, designing Ė_(z)(t)=−γ(t)Φ(E_(z)(t),t) and substituting equation (6) and its derivative Ė_(z)(t)={dot over (a)}_(z)(t)u₁(t)+a_(z)(t){dot over (u)}₁(t)+{dot over (b)}_(z)(t), so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

a _(z)(t){dot over (u)} ₁(t)=({dot over (a)} _(z)(t)u ₁(t)+{dot over (b)} _(z)(t)+γ(t)Φ(E _(z)(t),t))  (19)

the position z(t) and ż(t) will converge to a target z_(T)(t) and ż_(T)(t), respectively, in a super-exponential manner within finite time;

-   -   for the roll angle ϕ(t), according to the finite-time         varying-parameter convergence differential neurodynamics design         method, designing Ė_(ϕ)(t)=−γ(t)Φ(E_(ϕ)(t),t), and substituting         equation (10) and its derivative

${{{\overset{.}{E}}_{\phi}(t)} = {{\frac{l}{J_{x}}{{\overset{.}{u}}_{1}(t)}} + {{\overset{.}{b}}_{\phi}(t)}}},$

so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

$\begin{matrix} {{\frac{l}{J_{x}}{{\overset{.}{u}}_{2}(t)}} = {- \left( {{{\overset{.}{b}}_{\phi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\phi}(t)},t} \right)}}} \right)}} & (20) \end{matrix}$

the roll angle ϕ(t) and ϕ(t) will converge to a target ϕ_(T)(t) and {dot over (ϕ)}_(T)(t), respectively, in a super-exponential manner within finite time;

for the pitch angle θ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(θ)(t)=−γ(t)Φ(E_(θ)(t),t) and substituting equation (14) and its derivative

${{{\overset{.}{E}}_{\theta}(t)} = {{\frac{l}{J_{y}}{{\overset{.}{u}}_{3}(t)}} + {{\overset{.}{b}}_{\theta}(t)}}},$

so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

$\begin{matrix} {{\frac{l}{J_{y}}{{\overset{.}{u}}_{3}(t)}} = {- \left( {{{\overset{.}{b}}_{\theta}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\theta}(t)},t} \right)}}} \right)}} & (21) \end{matrix}$

the pitch angle θ(t) and {dot over (θ)}(t) will converge to a target θ_(T)(t) and {dot over (θ)}_(T)(t) respectively, in a super-exponential manner within finite time; and

for the yaw angle ψ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(ψ)(t)=−γ(t)Φ(E_(ψ)(t),t), and substituting equation (18) and its derivative

${{{\overset{.}{E}}_{\psi}(t)} = {{\frac{1}{J_{z}}{{\overset{.}{u}}_{4}(t)}} + {{\overset{.}{b}}_{\psi}(t)}}},$

so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained:

$\begin{matrix} {{\frac{l}{J_{z}}{{\overset{.}{u}}_{4}(t)}} = {- \left( {{{\overset{.}{b}}_{\psi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\psi}(t)},t} \right)}}} \right)}} & (22) \end{matrix}$

the pitch angle ψ(t) and {dot over (ψ)}(t) will converge to a target ψ_(T)(t) and {dot over (ψ)}_(T)(t). respectively, in a super-exponential manner within finite time; and

solving the synthesized control parameters u₁˜u₄ which is the control parameters corresponding to the flight demand of the aerial vehicle, according to equations (19), (20), (21) and (22), obtaining the neural network equations of the control parameters u₁˜u₄ respectively as follows:

$\begin{matrix} \left\{ \begin{matrix} {{{\overset{.}{u}}_{1}(t)} = \frac{- \left( {{{{\overset{.}{a}}_{z}(t)}{u_{1}(t)}} + {{\overset{.}{b}}_{z}(t)} + {{\gamma(t)}{\Phi\left( {{E_{z}(t)},t} \right)}}} \right)}{a_{z}(t)}} \\ {{{\overset{.}{u}}_{2} = {{- \left( {{b_{\phi}(y)} + {{\gamma(t)}{\Phi\left( {{E_{\phi}(t)},t} \right)}}} \right)}\frac{J_{x}}{l}}}\mspace{115mu}} \\ {{{\overset{.}{u}}_{3} = {{- \left( {{b_{\theta}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\theta}(t)},t} \right)}}} \right)}\frac{J_{y}}{l}}}\mspace{124mu}} \\ {{{\overset{.}{u}}_{4} = {{- \left( {{b_{\psi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\psi}(t)},t} \right)}}} \right)}J_{z}}}\mspace{124mu}} \end{matrix} \right. & (23) \end{matrix}$

and performing different output control assignments with the solved control parameters u₁(t)˜u₄(t) according to the structure of and the number of motors of different rotor aerial vehicles.

According to the control parameters u₁˜u₄ obtained in the above-mentioned neural network solving process, with regard to structures and motor numbers of different aerial vehicles, each motor is controlled through corresponding motor control parameter assignment, thus completing the motor control parameter assignment and motor control in the flow chart. According to the above steps, the invention can be achieved.

To sum up, the invention firstly acquires real-time flight orientation and attitude data of the multi-rotor unmanned aerial vehicle through sensors thereof, and analyzes and processes kinematic problems of the aerial vehicle correspondingly through an airborne processor to establish a dynamics model of the aerial vehicle; then, designs a finite-time varying-parameter convergence differential neural network solver for the dynamics model of the multi-rotor aerial vehicle according to a finite-time varying-parameter convergence differential neurodynamics design method; next, solves output control parameters of motors of the aerial vehicle through the finite-time varying-parameter convergence differential neural network solver using the acquired real-time orientation and attitude data of the aerial vehicle; and finally, transmits results to speed regulators of the motors of the aerial vehicle to control the motion of the unmanned aerial vehicle. Based on the finite-time varying-parameter convergence differential neurodynamics method, the invention can approximate the correct solution of the problem in a quick, accurate and real-time way, and can well solve a variety of time-varying problems such as matrix, vector, algebra and optimization.

The above-described embodiments are preferred embodiments of the invention; however, the embodiments of the invention are not limited to the above-described embodiments, and any other change, modification, replacement, combination, and simplification made without departing from the spirit, essence, and principle of the invention should be an equivalent replacement and should be included within the scope of protection of the invention. 

1. A stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics, the control method comprising the steps of: S1, acquiring real-time flight orientation and attitude data of the multi-rotor unmanned aerial vehicle through sensors thereof, and analyzing and processing kinematic problems of the aerial vehicle correspondingly through an airborne processor to establish a dynamics model of the aerial vehicle; S2, designing a finite-time varying-parameter convergence differential neural network solver for the dynamics model of the multi-rotor aerial vehicle according to a finite-time varying-parameter convergence differential neurodynamics design method; S3, solving output control parameters of motors of the aerial vehicle through the finite-time varying-parameter convergence differential neural network solver using the acquired real-time orientation and attitude data of the aerial vehicle; and S4, transmitting the solved output control parameters to speed regulators of the motors of the aerial vehicle to control the motion of the unmanned aerial vehicle.
 2. The stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics of claim 1, wherein the analyzing and processing kinematic problems of the aerial vehicle correspondingly through an airborne processor to establish a dynamics model of the aerial vehicle of step S1 specifically comprises: ignoring the effect of air resistance on the aerial vehicle, such that a physical model can be established for the aerial vehicle system: $\begin{matrix} {{{{\begin{bmatrix} {mI} & 0_{3 \times 3} \\ 0_{3 \times 3} & J \end{bmatrix}\begin{bmatrix} \overset{.}{v} \\ \overset{.}{w} \end{bmatrix}} + \begin{bmatrix} {w \times ({mv})} \\ {w \times ({Jw})} \end{bmatrix}} = {\begin{bmatrix} F \\ T \end{bmatrix} + \begin{bmatrix} G \\ 0_{3 \times 3} \end{bmatrix}}},} & (1) \end{matrix}$ wherein m is a total mass of the aerial vehicle, I is a 3×3 identity matrix, J is a rotational inertia matrix of the aerial vehicle, v and w are a velocity vector and an angular velocity vector of the aerial vehicle in a ground coordinate system, F and G are an axial component vector of an output resultant force of the motors of the aerial vehicle and an axial component vector of gravity of the aerial vehicle, respectively, and T is a rotational torque vector of the aerial vehicle; establishing a ground coordinate system X_(G) and an aerial vehicle body coordinate system X_(U), wherein the ground coordinate system and the body coordinate system have the following relationship: X_(U)=KX_(G), in which conversion relationship, K is a rotation conversion matrix between the ground coordinate system and the body coordinate system, which can be expressed as ${K = \begin{bmatrix} {C_{\theta}C_{\psi}} & {C_{\theta}S_{\psi}} & {- S_{\theta}} \\ {S_{\phi}S_{\theta}C_{\psi}} & {{S_{\phi}S_{\theta}S_{\psi}} + {C_{\phi}S_{\psi}}} & {S_{\phi}C_{\theta}} \\ {{S_{\phi}S_{\theta}C_{\psi}} - {C_{\phi}S_{\psi}}} & {{C_{\phi}S_{\theta}S_{\psi}} - {S_{\theta}C_{\psi}}} & {C_{\theta}C_{\phi}} \end{bmatrix}},$ wherein C_(θ) represents cos θ(t), S_(θ) represents sin θ(t), θ(t) is the pitch angle, ψ(t) is the yaw angle, and ϕ(t) is the roll angle; according to the coordinate conversion theory, in a translation direction and a rotation direction of the aerial vehicle, basing on the above physical model, such that the following dynamics equation in the aerial vehicle body coordinate system can be obtained $\begin{matrix} \left\{ \begin{matrix} {\overset{¨}{x} = \frac{{u_{1}(t)}\left( {{\cos\mspace{14mu}{\phi(t)}\mspace{14mu}\sin\mspace{14mu}{\theta(t)}\mspace{14mu}\cos\mspace{14mu}{\psi(t)}} + {\sin\mspace{14mu}{\theta(t)}\mspace{14mu}\sin\mspace{14mu}{\psi(t)}}} \right)}{m}} \\ {\overset{¨}{y} = \frac{{u_{1}(t)}\left( {{\sin\mspace{14mu}{\phi(t)}\mspace{14mu}\sin\mspace{14mu}{\theta(t)}\mspace{14mu}\cos\mspace{14mu}{\psi(t)}} - {\sin\mspace{14mu}{\psi(t)}\mspace{14mu}\cos\mspace{14mu}{\psi(t)}}} \right)}{m}} \\ {{\overset{¨}{z} = {\frac{{u_{1}(t)}\mspace{14mu}\cos\mspace{14mu}{\theta(t)}\mspace{14mu}\cos\mspace{14mu}{\phi(t)}}{m} - g}}\mspace{259mu}} \\ {{\overset{¨}{\phi} = \frac{{l \cdot {u_{2}(t)}} + {\left( {J_{y} - J_{z}} \right){\overset{.}{\psi}(t)}{\overset{.}{\theta}(t)}}}{J_{y}}}\mspace{265mu}} \\ {{\overset{¨}{\theta} = \frac{{l \cdot {u_{3}(t)}} + {\left( {J_{z} - J_{x}} \right){\overset{.}{\psi}(t)}{\overset{.}{\phi}(t)}}}{J_{y}}}\mspace{265mu}} \\ {{{\overset{¨}{\psi} = \frac{{u_{4}(t)} + {\left( {J_{x} - J_{y}} \right){\overset{.}{\theta}(t)}{\overset{.}{\phi}(t)}}}{J_{z}}},}\mspace{281mu}} \end{matrix} \right. & (2) \end{matrix}$ wherein x, y, z are position coordinates of the aerial vehicle in the world coordinate system, respectively, J_(x), J_(y) and J_(z) are rotational inertia of the aerial vehicle in x-axis, y-axis and z-axis directions, respectively, l is an arm length, g is gravitational acceleration, synthesized control parameters u₁˜u₄ consist of output thrust of the motors of the aerial vehicle and a synthesized torque, u₁(t) is a resultant force in a vertical ascending direction of the aerial vehicle, u₂ (t) is a resultant force in a roll angle direction, u₃(t) is a resultant force in a pitch angle direction, and u₄(t) is the synthesized torque in a yaw angle direction.
 3. The stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics of claim 2, wherein the designing a finite-time varying-parameter convergence differential neural network solver for the dynamics model of the multi-rotor aerial vehicle according to a finite-time varying-parameter convergence differential neurodynamics design method of step S2 specifically comprises: by means of the finite-time varying-parameter convergence differential neurodynamics design method, designing a system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄ in respect to the z-axis height z(t), the roll angle ϕ(t), the pitch angle θ(t) and the yaw angle ψ(t), respectively; and designing the finite-time varying-parameter convergence differential neural network solver according to the obtained system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄, respectively.
 4. The stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics of claim 3, wherein the step of by means of the finite-time varying-parameter convergence differential neurodynamics design method, designing a system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄ in respect to the z-axis height z(t), the roll angle ϕ(t), the pitch angle θ(t) and the yaw angle ψ(t), respectively, specifically comprises: S201, for the z-axis height z(t), according to a set target height value and an actual height value z_(T)(t) in the z-axis direction, defining a deviation function e_(z1) about the actual height value z(t) on a position layer as follows: e_(z1)(t)=z(t)−z_(T) (t) in order to enable the actual value z(t) to converge to the time-varying target value z_(T)(t), designing a neurodynamics equation ė_(z1)(t)=−γ(t)Φ(e_(z1)(t),t) based on a deviation function according to the finite-time varying-parameter convergence differential neurodynamics design method, wherein γ(t)=p+t^(p) is a time-varying parameter representing a regulatory factor for the rate of convergence; ${\Phi\left( {{e_{z\; 1}(t)},t} \right)} = {{k_{1}{{e_{z\; 1}(t)}}^{r}{{sign}\left( {e_{z\; 1}(t)} \right)}} + {k_{2}{e_{z\; 1}(t)}} + {k_{3}{{e_{z\; 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{z\; 1}(t)} \right)}}}$ according to the deviation function e_(z1)(t)=z(t)−z_(T) (t), ė_(z1)=ż(t)−ż_(T)(t) can be obtained; by substituting and e_(z1)(t)=z(t)−z_(T)(t)−z_(T)(t) and ė_(z1)(t)=ż(t)−ż_(T)(t) into ė_(z1) (t)=−γ(t)Φ(e_(z1)(t),t), we can obtain ż(t)−ż _(T)(t)+(t ^(p) +p)Φ(e _(z1)(t),t)=0.  (3) the position layer z(t) can converge to the time-varying target value z_(T)(t) in a super-exponential manner within a finite time, however, since equation (3) does not contain relevant information about the control parameters u₁˜u₄, the solution of the control parameters cannot be realized, therefore, it is necessary to further design the deviation function including a velocity layer ż(t) and an acceleration layer {umlaut over (z)}(t) thus defining e_(z2)(t)=ż(t)−ż_(T)(t)+(t^(p)+p)Φ(e_(z1)(t),t); according to the finite-time varying-parameter convergence differential neural network design method, the dynamics equation ė_(z2)(t)=−γ(t)Φ(e_(z2)(t),t) based on the deviation function can be designed, ${\Phi\left( {{e_{z\; 2}(t)},t} \right)} = {{k_{1}{{e_{z\; 2}(t)}}^{r}{{sign}\left( {e_{z\; 2}(t)} \right)}} + {k_{2}{e_{z\; 2}(t)}} + {k_{3}{{e_{z\; 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{z\; 2}(t)} \right)}}}$ according to e_(z2)(t)=ż(t)−ż_(T)(t)+(t^(p)+p)Φ(e_(z1)(t),t) the derivative ė_(z2)(t) of the deviation function e_(z2)(t) is known as: ė_(z2)={umlaut over (z)}(t)−{umlaut over (z)}_(T)(t)+(p+t^(p)){dot over (Φ)}(e_(z1)(t),t)+pt^(p−1)Φ(e_(z1)(t),t), by substituting the above equations about e_(z2) (t) and ė_(z2) (t) into the equation ė_(z2) (t)=−γ(t)Φ(e_(z2)(t),t) the following function can be obtained: {umlaut over (z)}(t)−{umlaut over (z)} _(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(z1)(t),t)+Φ(e _(z2)(t),t)+pt ^(p−1)Φ(e _(z1)(t),t)=0   (4) when equation (4) is established, the velocity layer ż(t) will converge to ż_(T) (t) within finite time in a super-exponential manner, according to which the deviation function can be considered E _(z)(t)={umlaut over (z)}(t)−{umlaut over (z)} _(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(z1)(t),t)+Φ(e _(z2)(t),t)+pt ^(p−1)Φ(e _(z1)(t),t)   (5) in order to obtain an actual model of the neural network, in combination with kinetic equation (2), equation (5) can be rewritten into E _(z)(t)=a _(z)(t)u ₁(t)+b _(z)(t)   (6) wherein ${{a_{z}(t)} = \frac{\cos\mspace{14mu}{\theta(t)}\mspace{14mu}\cos\mspace{14mu}{\phi(t)}}{m}},$ b_(z)(t)=−g−{umlaut over (z)}_(T)(t) (p+t^(p)){dot over (Φ)}(e_(z1)(t),t)+pt^(p−1)Φ(e_(z1)(t),t)+(p+t^(p))Φ(e_(z2)(t),t) that is, the deviation function about the output control parameter u₁(t) is obtained; S202, for the roll angle ϕ(t), in order to reach a target angle ϕ_(T)(t), first defining an error function e_(ϕ1)=ϕ(t)−ϕ_(T)(t), such that we can obtain ė_(ϕ1)={dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t), since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(ϕ1)(t)=−γ(t)Φ(e_(ϕ1)(t),t), ${{\Phi\left( {{e_{\phi 1}(t)},t} \right)} = {{k_{1}{{e_{\phi 1}(t)}}^{r}{{sign}\left( {e_{\phi 1}(t)} \right)}} + {k_{2}{e_{\phi 1}(t)}} + {k_{3}{{e_{\phi 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\phi 1}(t)} \right)}}}};$ by substituting the error function e_(ϕ1)(t) and ė_(ϕ1)(t) into the equation ė_(ϕ1)(t)=−γ(t)Φ(e_(ϕ1)(t),t), we can obtain {dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(t ^(p) +p)Φ(e _(ϕ1)(t),t)=0,   (7) ϕ(t) will converge to the target angle ϕ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (ϕ)}(t) is known, it is necessary to solve the equation involving {umlaut over (ϕ)}(t); in order to obtain the equation involving {umlaut over (ϕ)}(t), the error function e_(ϕ2)={dot over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(t^(p)+p)Φ(e_(ϕ1)(t),t) is set by the same method and ė_(ϕ2)(t)={umlaut over (ϕ)}(t)−{umlaut over (ϕ)}_(T)(t)+(p+t^(p)){dot over (Φ)}(e_(ϕ1)(t),t)+pt^(p−1)Φ(e_(ϕ1)(t),t) ${{\Phi\left( {{e_{\phi 2}(t)},t} \right)} = {{k_{1}{{e_{\phi 2}(t)}}^{r}{{sign}\left( {e_{\phi 2}(t)} \right)}} + {k_{2}{e_{\phi 2}(t)}} + {k_{3}{{e_{\phi 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\phi 2}(t)} \right)}}}};$ by substituting the above equations of e_(ϕ2)(t) and ė_(ϕ2)(t) into ė_(φ2) (t)=−γ(t)Φ(e_(φ2)(t),t), the following function can be obtained: {umlaut over (ϕ)}(t)−{umlaut over (ϕ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ϕ1)(t),t)+Φ(e _(ϕ2)(t),t)+pt ^(p−1)Φ(e _(ϕ1)(t),t)=0   (8) when equation (8) is established, the velocity layer {dot over (ϕ)}(t) will converge to {dot over (ϕ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered E _(ϕ)={umlaut over (ϕ)}(t)−{dot over (ϕ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ϕi)(t),t)+Φ(e _(ϕ2)(t),t)+pt ^(p−1)Φ(e _(ϕi)(t),t)   (9) when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into $\begin{matrix} {{{E_{\phi}(t)} = {{\frac{l}{J_{x}}{u_{2}(t)}} + {b_{\phi}(t)}}},} & (10) \end{matrix}$ wherein ${b_{\phi}(t)} = {\frac{\left( {J_{y} - J_{z}} \right){\overset{.}{\psi}(t)}{\overset{.}{\theta}(t)}}{J_{x}} - {{\overset{¨}{\phi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\phi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\phi 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\phi 2}(t)},t} \right)} \right)}}$ that is, the deviation function about the output control parameter u₂(t) is obtained; S203, for the pitch angle θ(t), in order to reach a target angle θ_(T)(t), first defining an error function e_(θ1)=θ(t)−θ_(T)(t), such that we can obtain ė_(θ1)={dot over (θ)}(t)−{dot over (θ)}_(T)(t); since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(θ1)(t)=−γ(t)Φ(e_(θ1)(t),t) ${{\Phi\left( {{e_{\theta 1}(t)},t} \right)} = {{k_{1}{{e_{\theta 1}(t)}}^{r}{{sign}\left( {e_{\theta 1}(t)} \right)}} + {k_{2}{e_{\theta 1}(t)}} + {k_{3}{{e_{\theta 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\theta 1}(t)} \right)}}}};$ by substituting the error function e_(θ1)(t) and ė_(θ1)(t) into the equation ė_(θ1)(t)=−γ(t)Φ(e_(θ1)(t),t), we can obtain {dot over (θ)}(t)−{dot over (θ)}_(T)(t)+(t ^(p) +p)Φ(e _(θ1)(t),t)=0,   (11) θ(t) will converge to the target angle θ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (θ)}(t) is known, it is necessary to solve the equation involving {umlaut over (θ)}(t); in order to obtain the equation involving {umlaut over (θ)}(t), the error function e_(θ2)={dot over (θ)}(t)−{dot over (θ)}_(T)(t)+(t^(p)+p)Φ(e_(θ1)(t),t) is set by the same method and ė_(θ2)(t)={umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t^(p)){dot over (Φ)}(e_(θ1)(t)t), pt^(p−1)Φ(e_(θ1)(t),t), ${{\Phi\left( {{e_{\theta 2}(t)},t} \right)} = {{k_{1}{{e_{\theta 2}(t)}}^{r}{{sign}\left( {e_{\theta 2}(t)} \right)}} + {k_{2}{e_{\theta 2}(t)}} + {k_{3}{{e_{\theta 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\theta 2}(t)} \right)}}}};$ by substituting the above equations of e_(θ2)(t) and ė_(θ2)(t) into the equation ė_(θ2)(t)=−γ(t)Φ(e_(θ2)(t),t), the following function can be obtained: {umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(θi)(t),t)+Φ(e _(θ2)(t),t)+pt ^(p−1)Φ(e _(θ1)(t),t)=0   (12) when equation (12) is established, the velocity layer {dot over (θ)}(t) will converge to {dot over (θ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered E _(θ)(t)={umlaut over (θ)}(t)−{umlaut over (θ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(θ1)(t),t)+Φ(e _(θ2)(t),t)+pt ^(p−1)Φ(e _(θ1) ,t),t)   (13) when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into $\begin{matrix} {{{E_{\theta}(t)} = {{\frac{l}{J_{y}}{u_{3}(t)}} + {b_{\theta}(t)}}},} & (14) \end{matrix}$ wherein ${{b_{\theta}(t)} = {\frac{\left( {J_{z} - J_{x}} \right){\overset{.}{\psi}(t)}{\overset{.}{\phi}(t)}}{J_{y}} - {{\overset{¨}{\phi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\theta 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\theta 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\theta 1}(t)},t} \right)} \right)}}},$ that is, the deviation function about the output control parameter u₃(t) is obtained; and S204, for the yaw angle ψ(t), in order to reach a target angle ψ_(T)(t), first defining an error function e_(ψ1)=ψ(t)−ψ_(T)(t), such that we can obtain ė_(ψ1)={dot over (ψ)}(t)−{dot over (ψ)}_(T)(t); since the solution is in an angle layer, according to the finite-time varying-parameter differential neurodynamics design method, we can obtain ė_(ψ1)(t)=−γ(t)Φ(e_(ψ1)(t),t), ${{\Phi\left( {{e_{\psi 1}(t)},t} \right)} = {{k_{1}{{e_{\psi 1}(t)}}^{r}{{sign}\left( {e_{\psi 1}(t)} \right)}} + {k_{2}{e_{\psi 1}(t)}} + {k_{3}{{e_{\psi 1}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\psi 1}(t)} \right)}}}};$ by substituting the error function e_(ψ1)(t) and ė_(ψ1)(t) into the equation ė_(ψ1)(t)=−γ(t)Φ(e_(ψ1) (t),t) we can obtain {dot over (ψ)}(t)−{dot over (ψ)}(t)+(t ^(p) +p)Φ(e _(ψ1)(t),t)=0,   (15) ψ(t) will converge to the target angle ψ_(T)(t) in a super-exponential manner within finite time; since {umlaut over (ψ)}(t) is known, it is necessary to solve the equation involving {umlaut over (ψ)}(t); in order to obtain the equation involving {umlaut over (ψ)}(t), the error function e_(ψ2)={dot over (ψ)}(t)−{dot over (ψ)}_(T)(t)+(t^(p)+p)Φ(e_(ψ1)(t),t) is set by the same method and ${{{\overset{.}{e}}_{\psi 2}(t)} = {{\overset{¨}{\psi}(t)} - {{\overset{¨}{\psi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\psi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\psi 1}(t)},t} \right)}}}},{{{\Phi\left( {{e_{\psi 2}(t)},t} \right)} = {{k_{1}{{e_{\psi 2}(t)}}^{r}{{sign}\left( {e_{\psi 2}(t)} \right)}} + {k_{2}{e_{\psi 2}(t)}} + {k_{3}{{e_{\psi 2}(t)}}^{\frac{1}{r}}{{sign}\left( {e_{\psi 2}(t)} \right)}}}};}$ by substituting the above equations of e_(ψ2)(t) and ė_(ψ2)(t) into ė_(ψ2)(t)=−γ(t)Φ(e_(ψ2)(t),t), the following function can be obtained: {umlaut over (ψ)}(t)−{umlaut over (ψ)}_(T)(t)+(p+t ^(p)){dot over (Φ)}(e _(ψ1)(t),t)+Φ(e _(ψ2)(t),t)+pt ^(p−1)101(e _(ψ1)(t),t=0   (16) when equation (16) is established, the velocity layer {dot over (ψ)}(t) will converge to {dot over (ψ)}_(T)(t) within finite time in a super-exponential manner, according to which the deviation function can be considered E _(ψ)(t)={umlaut over (ψ)}(t)−{umlaut over (ψ)}T(t)+(p+t ^(p)){dot over (Φ)}(e _(ψ1)(t),t)+Φ(e _(ψ2)(t),t)+pt ^(p−1)Φ(e _(ψ1)(t),t)   (17) when the aerial vehicle reaches a target state, according to the dynamics model equation, the deviation function can be converted into $\begin{matrix} {{{E_{\psi}(t)} = {{\frac{l}{J_{z}}{u_{4}(t)}} + {b_{\psi}(t)}}},} & (18) \end{matrix}$ wherein ${{b_{\psi}(t)} = {\frac{\left( {J_{x} - J_{y}} \right){\overset{.}{\phi}(t)}{\overset{.}{\theta}(t)}}{J_{z}} - {{\overset{¨}{\psi}}_{T}(t)} + {\left( {p + t^{p}} \right){\overset{.}{\Phi}\left( {{e_{\psi 1}(t)},t} \right)}} + {{pt}^{p - 1}{\Phi\left( {{e_{\psi 1}(t)},t} \right)}} + {\left( {p + t^{p}} \right)\left( {\Phi\left( {{e_{\psi 2}(t)},t} \right)} \right)}}},$ that is, the deviation function about the output control parameter u₄(t) is obtained.
 5. The stable flight control method for a multi-rotor unmanned aerial vehicle based on finite-time neurodynamics of claim 4, wherein the step of designing the finite-time varying-parameter convergence differential neural network solver according to the obtained system parameter deviation function of the finite-time varying-parameter convergence differential neural network about the output control parameters u₁˜u₄, respectively, specifically comprises: S211, for the z-axis height z(t), by using the finite-time varying-parameter convergence differential neural network design method, designing Ė_(z)(t)=−γ(t)Φ(E_(z)(t),t) and substituting equation (6) and the derivative Ė_(z)(t)={dot over (a)}_(z)(t)u₁(t)+a_(z)(t){dot over (u)}₁(t)+{dot over (b)}_(z)(t), so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained: a _(z)(t){dot over (u)} ₁(t)=−({dot over (a)} _(z)(t)u ₁(t)+{dot over (b)} _(z)(t)+γ(t)Φ(E _(z)(t),t))   (19) the position z(t) and velocity ż(t) will converge to a target position z_(T)(t) and a target velocity ż_(T)(t), respectively, in a super-exponential manner within finite time; S212, for the roll angle ϕ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(ϕ)(t)=−γ(t)Φ(E_(ϕ)(t),t), and substituting equation (10) and its derivative ${{{\overset{.}{E}}_{\phi}(t)} = {{\frac{l}{J_{x}}{{\overset{.}{u}}_{1}(t)}} + {{\overset{.}{b}}_{\phi}(t)}}},$ so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained: $\begin{matrix} {{\frac{l}{J_{x}}{{\overset{.}{u}}_{2}(t)}} = {- \left( {{{\overset{.}{b}}_{\phi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\phi}(t)},t} \right)}}} \right)}} & (20) \end{matrix}$ the roll angle ϕ(t) and velocity {dot over (ϕ)}(t) will converge to a target position ϕ_(T)(t) and a target velocity {dot over (ϕ)}_(T)(t), respectively, in a super-exponential manner within finite time; S213, for the pitch angle θ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(θ)(t)=−γ(t)Φ(E_(θ)(t),t) and substituting equation (14) and its derivative ${{{\overset{.}{E}}_{\theta}(t)} = {{\frac{l}{J_{y}}{{\overset{.}{u}}_{3}(t)}} + {{\overset{.}{b}}_{\theta}(t)}}},$ so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained: $\begin{matrix} {{\frac{l}{J_{y}}{{\overset{.}{u}}_{3}(t)}} = {- \left( {{{\overset{.}{b}}_{\theta}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\theta}(t)},t} \right)}}} \right)}} & (21) \end{matrix}$ the pitch angle θ(t) and velocity {dot over (θ)}(t) will converge to a target position θ_(T)(t) and a target velocity {dot over (θ)}_(T)(t), respectively, in a super-exponential manner within finite time; S214, for the yaw angle ψ(t), according to the finite-time varying-parameter convergence differential neurodynamics design method, designing Ė_(ψ)(t)=−γ(t)Φ(E_(ψ)(t),t), and substituting equation (18) and its derivative ${{{\overset{.}{E}}_{\psi}(t)} = {{\frac{1}{J_{z}}{{\overset{.}{u}}_{4}(t)}} + {{\overset{.}{b}}_{\psi}(t)}}},$ so that an implicit dynamics equation of the finite-time varying-parameter convergence differential neural network can be obtained: $\begin{matrix} {{\frac{1}{J_{z}}{{\overset{.}{u}}_{4}(t)}} = {- \left( {{{\overset{.}{b}}_{\psi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\psi}(t)},t} \right)}}} \right)}} & (22) \end{matrix}$ the pitch angle ψ(t) and velocity {dot over (ψ)}(t) will converge to a target position ψ_(T)(t) and a target velocity {dot over (ψ)}_(T)(t), respectively, in a super-exponential manner within finite time; and S215, solving the synthesized control parameters u₁˜u₄ which is the control parameters corresponding to the flight demand of the aerial vehicle, according to equations (19), (20), (21) and (22), obtaining the neural network equations of the control parameters u₁˜u₄ respectively as follows: $\begin{matrix} \left\{ \begin{matrix} {{{\overset{.}{u}}_{1}(t)} = \frac{- \left( {{{{\overset{.}{a}}_{z}(t)}{u_{1}(t)}} + {{\overset{.}{b}}_{z}(t)} + {{\gamma(t)}{\Phi\left( {{E_{z}(t)},t} \right)}}} \right)}{a_{z}(t)}} \\ {{{\overset{.}{u}}_{2} = {{- \left( {{b_{\phi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\phi}(t)},t} \right)}}} \right)}\frac{J_{x}}{l}}}\mspace{121mu}} \\ {{{\overset{.}{u}}_{3} = {{- \left( {{b_{\theta}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\theta}(t)},t} \right)}}} \right)}\frac{J_{y}}{l}}}\mspace{124mu}} \\ {{{\overset{.}{u}}_{4} = {{- \left( {{b_{\psi}(t)} + {{\gamma(t)}{\Phi\left( {{E_{\psi}(t)},t} \right)}}} \right)}J_{z}}}\mspace{124mu}} \end{matrix} \right. & (23) \end{matrix}$ and performing different output control assignments with the solved control parameters u₁·u₄ according to the structure of and the number of motors of different rotor aerial vehicles. 